Highly Accurate Method for Boundary Value Problems with Robin Boundary Conditions

The main aim of the current paper is to construct a numerical algorithm for the numerical solutions of second-order linear and nonlinear differential equations subject to Robin boundary conditions. A basis function in terms of the shifted Chebyshev polynomials of the first kind that satisfy the homo...

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Bibliographic Details
Published inJournal of nonlinear mathematical physics Vol. 30; no. 3; pp. 1239 - 1263
Main Author Ahmed, Hany. M.
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.09.2023
Springer Nature B.V
Subjects
Algorithms
Basis functions
Boundary conditions
Boundary value problems
Chebyshev approximation
Collocation methods
Exact solutions
Mathematical Physics
Mathematics
Mathematics and Statistics
Methods
Nonlinear differential equations
Numerical analysis
Polynomials
Research Article
34B05
Boundary value problems
65L60
Chebyshev polynomials of the first kind
Robin boundary conditions
Collocation method
Generalized hypergeometric functions
42C05
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Summary:The main aim of the current paper is to construct a numerical algorithm for the numerical solutions of second-order linear and nonlinear differential equations subject to Robin boundary conditions. A basis function in terms of the shifted Chebyshev polynomials of the first kind that satisfy the homogeneous Robin boundary conditions is constructed. It has established operational matrices for derivatives of the constructed polynomials. The obtained solutions are spectral and are consequences of the application of collocation method. This method converts the problem governed by their boundary conditions into systems of linear or nonlinear algebraic equations, which can be solved by any convenient numerical solver. The theoretical convergence and error estimates are discussed. Finally, we support the presented theoretical study by presenting seven examples to ensure the accuracy, efficiency, and applicability of the constructed algorithm. The obtained numerical results are compared with the exact solutions and results from other methods. The method produces highly accurate agreement between the approximate and exact solutions, which are displayed in tables and figures.
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ISSN:1776-0852
1402-9251
1776-0852
DOI:10.1007/s44198-023-00124-6